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Joint Institute for Nuclear Research, Dubna, Russia International SCHOOL on Nuclear Fission and related phenomena May 13 -24 2014, VECC Kolkata Avazbek NASIROV * Nuclear Reaction Mechanisms in Heavy Ion Collisions (Lecture I) 13 May 2014 *Institute of Nuclear Physics, Tashkent, Uzbekistan 1

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Contents 1. Introduction. 2. Main properties of nuclei which determine the characteristics of reaction products. 3. Reaction channels in heavy ion collisions at low energies, at energies near the Coulomb barrier of interaction. 4. Interesting problems in study of nuclear reaction mechanism. 5. Ternary fission and true ternary fission

Mendeleev periodic table of the elements (2014)

Introduction

Heavy ions are many body system Atomic nucleus is a quantum object which consists from protons and neutrons binding by strong nucleon -nucleon interaction. The reaction taking place in collisions of atomic nuclei should be described adequately. The application of classical picture requires consideration of nucleus as localized wave packets. The role of the electron shell is not so important in nucleus-nucleus interaction because of smallness of the electron’s mass me/m. N=0. 0005.

Mass excess, binding energy and energy balance Mass excess Δm(A, Z)=M(A, Z) - A·u (1) M(A, Z) is the mass of nucleus and A is its mass number. ; u is mass units u=M 12 C/12=931. 502 Me. V; or (2) u= 1660538. 73(0. 13)10 -33 kg Mp=7. 289 Me. V; Mn=8. 071 Me. V; Measured total mass M(A, Z) E, v (3) M(A, Z)

Mass excess Δm(A, Z)=M(A, Z) - A·u (1) u=931. 502 Me. V Binding energy per nucleon : B/A = [ZMp+NMn−M(A, Z)]/A. (2) Binding energy B(A, Z)=Δm(A, Z)-Z·Mp -N·Mn (3) Let us find connection between Δm mass excess and binding energy per nucleon: Δm(A, Z)=M(A, Z) - A·u= ZMp+NMn- (B/A) A- A·u Δm(A, Z)= ZMp+NMn- ((B/A) –u) · A (4)

Using the atomic mass table Δm B/A Δm(A, Z)= ZMp+NMn- ((B/A) –u) · A

Energy balance of reaction Qgg= B(A 1, Z 1)+B(A 2, Z 2)-Bcn(A 1+A 2, Z 1+Z 2)= Δm (A 1, Z 1)+Δm (A 2, Z 2)- Δm (A 1+A 2, Z 1+Z 2)Z 1·Mp –N 1·Mn –Z 2·Mp –N 2·Mn+(Z 1+Z 2) ·Mp + (N 1+N 2)·Mn. Qgg =Δm (A 1, Z 1)+Δm (A 2, Z 2)-Δm (A 1+A 2, Z 1+Z 2) (5) So, in our calculations we use the mass excess of nuclei presented in the atomic mass tables Audi, Wapstra

1. P. Möller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 2. Muntian, Z. Patyk, and A. Sobiczewski, Phys. At. Nucl. 66, 1015 (2003). 3. M. Kowal, P. Jachimowicz, and A. Sobiczewski, Phys. Rev. C 82, 014303 (2010).

Comparison of realized energy in chemical reactions (atomic scale) and nuclear fission (nuclear scale). Moleculas size is some factors of 1 Angstrem=10 -10 m Nuclear size is some orders of 1 fm=10 -15 m

Heat at burning of hydrogen and carbon Heat is evolved in the chemical reaction in which hydrogen and oxygen are combined to be water and generates 3. 0 e. V energy emission: Such chemical reaction in which heat is evolved is called exothermic reaction (exo - “outside”). Another example is where one mol of carbon is oxidated to be carbon dioxide with producing 4. 1 e. V energy : C+O 2= CO 2+ 4. 1 e. V (2) Electron – Volt (e. V) is a unit of energy extensively used in the atomic and nuclear world. It is the work done on an electron that is accelerated through a potential difference of one volt. "the energy evolved from one process of an exothermic chemical reaction is about 3 or 4 e. V".

Photosynthesis- Endothermic reaction 6 H 2 O+6 CO 2+ γ =C 6 H 12 O 6+6 O 2 γ C 6 H 12 O 6 O 2 D-Glucose (Sugar) The sun is a giant source of energy and plants are accumulator of its energy. But the efficiency of this way is not so high. (endo – “inside”) CO 2 C 6 H 12 O 6

Exothermic Nuclear Reactions Nuclei show various types of reaction: For example, one nuclide splits into two or more fragments. This type of reaction is called nuclear fission. Where is the exothermic heat energy coming from? The heat comes from the energy stored in the nuclear binding energies of the reactant nuclei. The binding energies of initial nuclei are greater than the energy stored in the binding energies of the reaction products. Contrarily, two nuclides sometimes combine with each other to be a new nuclide. This type of reaction is called nuclear fusion. There are many other types of reaction processes; they are generally called nuclear reactions. Among these various types of nuclear reactions, there are some types of exothermic reactions which are sometimes called "exoergic" reaction in nuclear physics. In endothermic reactions, the situation is reversed: more binding energy is stored in the reaction products than in the reactants nuclei.

Cold fusion-fission reaction mp=7. 289 Me. V, m. Li=14. 908 Me. V, m. He=2. 424 Me. V

Mechanism of releasing nuclear energy. Reaction energy balance Q is determined by mass difference between the initial and final sets of particles a) If Q > 0, reaction is exothermic (energy released as kinetic energy and g-rays). b) If Q <0, reaction is endothermic. There is a threshold of the energy of the incoming particle to make the reaction happen. c) Q =0 is elastic scattering. Total kinetic energy is conserved

Exothermic Nuclear Reactions • C+O 2= CO 2+ 4. 1 e. V (2) The nuclear reaction energy is million times more than energy of chemical reactions !

The neutron with thermal energy (En= 0, 025 e. V) causes excitation and fission of atomic nuclei Energy balance in nuclear fission 144 Ba+89 Kr channel: Qgg=m. U-m. Ba-m. Kr=215. 154 Me. V 236 U ⇾ Δm. U=42. 44 Me. V; BU/A= 7. 586 BU=42. 44 -92· 7. 289 -144· 8. 071=-1790. 372 Me. V; Δm. Ba=-71. 78 Me. V; BBa/A= 8. 265 BBa=-71. 78 -56· 7. 289 -88· 8. 071=-1190. 212 Me. V; Δm. Kr=-76. 72 Me. V; BKr/A= 8. 617 BKr=-76. 72 -36· 7. 289 -53· 8. 071=-766. 887 Me. V;

Fission induced by protons M Z + M 1 + M 2 Z 1 + Z 2 The source of the kinetic energy of products is intrinsic binding energy of system

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Calculation of the binding energy of nuclei av=15. 494 Me. V, as=17. 9439 Me. V, kv=1. 8 and ks=2. 6.

P. J. Siemens, A. S. Jensen, Elements of Nuclei, Lecture Notes and Supplements in Physics (Addison-Wesley, Redwood City, California, 1987).

Deformation energy in the liquid drop model

Fission Energy Distribution In the fission process, the fragments and neutrons move away at high speed carrying with them large amounts of kinetic energy. The neutrons released during the fission process are called fast neutrons because of their high speed. Neutrons and fission fragments fly apart instantaneously in a fission process. • Gamma rays (photons) equivalent to 8 Me. V of energy are released within a microsecond of fission. • The two fragments are beta emitters. Recall that beta decays are accompanied by antineutrino emissions, and the two types of particles carry away approximately equal amounts of energy. Estimated average values of various energies are given in a table: Energy (Me. V) distribution in fission reactions Kinetic energy of fission fragments 167 Me. V Prompt (< 10 -6 s) gamma ray energy 8 Kinetic energy of fission neutrons 8 Gamma ray energy from fission products 7 Beta decay energy of fission products 7 Energy as antineutrinos (ve) 7

Mass distribution of the fission products obtained by liquid drop model is symmetric because minimum values of the potential energy surface calculated by this model correspond to the mass symmetric region.

Kinetic energy of fission products transformed into kinetic energy of vapor

Mass and total energy distribution of the fission fragments. E. M. Kozulin. Intern. Conference Fusion 2006, Venezia. Prpjection of 3 D figure

Mass distribution of the fission products as a function of the excitation energy of compound nucleus E. M. Kozulin. Intern. Conference Fusion 2006, Venezia.

Asymmetric and Symmetric mass distributions of fission products as a function of the neutron numb 110 130 150110 130 150 37

Fission of nuclei 1. Spontaneous fission; 2. Fission induced by neutrons, gamma quantum, protons; 3. Fusion-fission reactions;

Spontaneous fission properties and lifetime systematics. Nucl. Phys. A 502 (1989) 21 c 40 c. 39

Ternary fission and true ternary fission • Ternary fission is an emission light charged nuclei (cluster) from the neck region. The probability of such decay decreases strongly by increase of the charge number of cluster. • True ternary fission is the decay of atomic nuclei into 3 fragments with comparable masses. The third emitted cluster may be nuclei with Z > 14. So true ternary fission can be considered as a bridge process between binary fission and cluster radioactivity.

Observation of the very asymmetric fission products Yields of such heavy clusters, as Fe, Ni, Zn and Ge were observed in very asymmetric fission. We can state the presence of two ways leading to formation of these clusters. 1. A. A. Goverdovsky et al. , Physics of Atomic Nuclei (Yadernaya Fizika) v. 58 (1995) p. 1546. 2. R. H. Iyer, et al. Proc. of Int. Symp. on Phys and Chem. of Fission, Julich, 1979, Vienna, IAEA, 1980, v. 2, p. 311. 3. Rao et al. Phys. Rev. C 37 ( ? ). 4. G. Barreau, et al. Nucl. Phys. A 432 (1985) p. 411. 5. Sida J. L. Nucl. Phys. A 502 (1989) p. 233 c. The authors of ref 1 noted that conclusion about charge Z=28 of the products with masses A=70 was made firstly by authors of the paper ref 2. [1] [2] [3] [4]

М 1 М 2 М 3 Prepared by Prof. Wolfram von Oertzen

Ternary fission with emission of alpha – particles is well known process. The one event of this mechanism occurs per approximately 260 events of binary fission [16] The angular distribution of the a particle, which is peaked nearly orthogonal to the direction of the main fragments, is understood qualitatively by assuming a particle separation close to the instant of scission where the Coulomb field of the nascent pair of fragments has still a focusing character. 1 A. V. Daniel et. al. , Phys. Rev. C 69 041305(R) (2004) 2. G. M. Ter-Akopian et al. , Phys. At. Nuclei 67, 1860 (2004). 3. A. V. Ramayya et al. , Rhys. Rev. C 57, 2370 (1998). 4. J. H. Hamilton et al. , Prog. Part. Nucl. Phys. 38, 273 (1997). 5. I. D. Alkhazov, et al, Sov. J. Nucl. Phys. 57, 978 (1988). 6. S. Oberstedt et al. , Nucl. Phys. A 761, 173 (2005).

TRUE TERNARY FISSION This mechanism of the ternary fission was early considered by Diehl and Greiner: Diehl H. , Greiner W. Ternary fission in the liquid drop model, Phys. Lett. B. 45 (1973) 35. Diehl H. , Greiner W. , Theory of ternary fission in the liquid drop model, Nucl. Phys. A. 229 (1974) 29.

Two possible mechanisms of the collinear cluster tri-partition of massive nuclei. Smallness of the kinetic energy of The middle fragment was study in Ref:

Experimental setup

Experimental results to study fission mechanism and role of the nuclear structure In the experiment they measure kinetic energy and velocity, angular distributions of the fragments, neutron multiplicity and energy spectra, as well as gamma multiplicity accompanying fission fragments.

Calculations of the potential energy surface. U 13=Vnucl(13) +Vcoul(13) U 32=Vnucl(32)+Vcoul(32) U 12=VCoul(12) R 1 2 1 B 1, B 2, B 3 and BCN are binding energies R 1 of fragments and fissioning nucleus, respectively. 2 3 2 R 3 2 49

Correspondence between minima of PES and yields of true ternary fission fragments of 252 Cf. A. K. Nasirov et al. Physics Scripta 89 (2014) 054022

• • • Asymmetric mass distribution of fission fragments is connected with the fact that atomic nuclei have shell structure. The properties of atomic nucleus differ from the properties of continuum system as water or honey. At fission of the continuum system two mass symmetric products are formed. But mass symmetric distribution of the fission products does not mean we deal with liquid drop like fissioning nucleus. Shell structure of atomic nucleus appears very strongly in nuclear reactions. We should keep in mind that atomic nucleus consists from protons and neutrons having close masses and spins equal ½ (fermions). But proton and neutron has different electric charges, +1 and 0, respectively.

Example of mixing products formed in the different reaction channels

Classification of the nuclear reactions in heavy ion collisions Early studies of reaction mechanisms between heavy ions have shown that, in a Wilczynski diagram, a definite evolution towards negative scattering angles with increasing energy loss is present, so that the scattering angle was used as an estimate of the interaction time. As usual three regions can be distinguished: (i) the elastic or quasi-elastic component; Eloss < 5 Me. V (ii) the partially damped region where the nuclear forces bend the trajectories toward smaller scattering angles; 5 Me. V < Eloss (iii) capture reactions (the fully relaxed component, where negative angle scattering or orbiting, fusion-fission and symmetric fragmentation may occur); 5 <Eloss < 50 Me. V Eloss is connected with nuclear excitation and emission of neutrons and particles. (iv) Fission of massive projectile nucleus by the target Coulomb field (collisions inverse kinematic).

Main characteristics of reaction products which is observed. G. Guarino et al. ,

G. Guarino et al. ,

Effect of nuclear shell structure on the reaction mechanisms in heavy ion collisions.

Effect of nuclear shell structure on the reaction mechanisms in heavy ion collisions. Deep inelastic collisions are very convenient to study reaction mechanism in heavy ion interaction since the nuclei are not destroyed strongly but main properties of the nuclear matter are already exhibited. Experiments showed that mass and charge distributions are very sensitive to shell structure. G. Guarino et al. ,

Direct reactions Only a few nucleons or excitation modes are involved in the so-called direct reactions (stripping reaction is presented). Projectile X+A=B+y x Reaction products B and y X=y+z B=A+z Target B The aim of experiment or calculations is to find cross section of the processes, angular and energy distributions of the final fragments. For example, separation energy of protons and neutrons, demonstrating shell structure, are determined in these reactions

Separation energies of protons and neutrons.

Multinucleon transfer is inherent to the capture reactions where full momentum transfer takes place.

Difference between deep-inelastic collisions and capture events • ΔE Vmin Bqf. L=0 It is important relations between ΔE and difference Ec. m. –Vmin as well as between Ec. m. –Vmin and depth of the potential well Bqf.

Comparison of the friction coefficients calculated by the different methods -- Gross-Kalinovski Solid line – semi-microscopic method Linear response theory by Yamaji Long dashed __ Temperature= 2 Мэ. В Short dashed. - - Temperature = 1 Мэ. В Dotted …. Temperature = 0. 5 Мэ. В Phys. Rev. C 56 No. 2, (1997) p. 373 -380 64

The friction coefficient depends on the relative distance between centers of nuclei and increases by temperature of nuclei. Dotted curve …. . . Incoming path ___ Outgoing path Solid curve 65

P P’ T Heavy ion collisions T’ Cap ture Deep – inelastic collisions ss Quasifi (I) ion (II) P” T” Dinuclear system F 1 F 2 (III) sion Fast fis Mononucleus Ec. m. =Elab F 1 Co fus mpl ion ete F 2 ( I V) (V) g in ol Co Compound nucleus sion s i f n o i Fus ER (ELab , L) = cap(ELab , L) PCN(ELab , L) Wsurv (ELab , L { } Evaporation residues

Potential energy surface of dinuclear system a- entrance channel; b-fusion channel; c and d are quasifission channels G. Giardina, S. Hofmann, A. I. Muminov, and A. K. Nasirov, Eur. Phys. J. A 8, 205– 216 (2000) Udr (A, Z, , ß 1 , ß 2 ) = B 1 + B 2 + V (A, Z, ß 1 ; ß 2 ; R) - BC N - VC N (L )

Nucleus-nucleus interaction potential 69

Fission products 70

Capture and fusion cross sections for the 48 Ca+238 U reaction. W. Q. Shen et al Phys. Rev. C 36. 115 (1987) GSI experiment Yu. Ts Oganessian et al, Phys. Rev. C 70 064609 (2004) G. G. Adamian, G. Giardina, A. K. Nasirov, in Cont. of "XIV Int. Workshop on Nuclear Fission" Physics, Obninsk, 1998, Russia, 2000

Results of calculation and comparison of them with the experimental data for the “cold” 64 Ni+208 Pb and 70 Zn+208 Pb reactions. * RIKEN G. Giardina, et al. Eur. Phys. J. A 8, 205– 216 (2000) * GSI S. Hofmann, Rep. Progr. Phys. 61, 639 (1998);

Importance of the shell effects in compound nuclei in formation of evaporation residues-superheavy elements (SHE) A - Cold fusion ZX=Cr, A ZX Fe, Ni, Zn +208 Pb, 209 Bi Hot fusion reactions 48 Ca+U, Pu, Cm, Cf 73

Potential energy surface of dinuclear system a- entrance channel; b-fusion channel; c and d are quasifission channels G. Giardina, S. Hofmann, A. I. Muminov, and A. K. Nasirov, Eur. Phys. J. A 8, 205– 216 (2000) Udr (A, Z, , ß 1 , ß 2 ) = B 1 + B 2 + V (A, Z, ß 1 ; ß 2 ; R) - BC N - VC N (L )

Conclusions 1) Two center shape of the mass and charge distributions are appearance of the shell structure of colliding nuclei and being formed fragments at low energies. 2) Peculiarities of the reaction channels are determined by mass and charge asymmetry of colliding nuclei and their orientation angles (if they are deformed).